A sound and complete semantics for propositionally quantified relevant logics

Abstract

The Routley-Meyer relational semantics for relevant logics are extended to give general-frame semantics for many propositionally quantified relevant logics (and some non-relevant ones). These semantics are shown to be both sound and complete with respect to each of the corresponding logical systems. It is then shown that use of a primary interpretation for the quantifier on the Routley-Meyer semantics causes incompleteness for many of the systems considered, in particular those that are sub-logics of Anderson and Belnap's system of entailment with mingle and constant t, EM t"p.